You should be able to send a text while you're in conversation because I do it all the time from my Android device. Now if you're trying to access the web while in conversation, then you will not be able to do so. If Facebook hasn't been successfully added to your account, then follow the steps below to do so.
1. From the Home screen, press the Menu Key , touchSettings, and touch Accounts & sync.The Accounts & sync settings screen displays your current sync settings and accounts.
2. Touch the Add account button.
3. Touch the account you want to add.
4. Follow the onscreen steps to enter the required (and optional) account information.
Many accounts require only a username and password, but some accounts will require more information. These sections also describe how to add an email account that uses IMAP, POP3, or SMTP.
5. Configure the account. Depending on the kind of account, you may be asked to
configure what kinds of data you want to sync to the phone, name of the account, and other details. When you're finished, the account will be added to the list in the Accounts & sync settings screen.
Let me know if this works for you
